The invention relates to signal representation and processing, particularly to signal representation and processing using local signal behavior parameters.
The standard method of signal processing uses representation of band-limited signals by Nyquist rate samples. Unique determination of band-limited signals requires a sequence of Nyquist rate samples from the entire interval (xe2x88x92∞, ∞). Moreover, such a sequence contains no redundant information, because by Nyquist""s Theorem for arbitrary sequence of real numbers {am}m=z such that             ∑              m        =                  -          ∞                    ∞        ⁢          xe2x80x83        ⁢          a      m      2         less than   ∞
there exists a xcfx80 band-limited signal f(t) such that f(m)=am. Of course, in practice operators act (essentially) on a sequence of approximations of the input signal obtained using a suitable moving window and setting the values of the signal to 0 at all sampling points outside of the support of the window.
Historically, numerical signal processing is older than the use of digital computers. For example, fast Fourier transforms (FFT) were first performed by hand. Also, early hardware for data acquisition (A/D conversion) and for numerical data processing was very limited in speed and capacity. In such circumstances it was important that the signal be represented without any redundancy and that the implementations of signal processing operators required minimal number of basic arithmetical operations. This determined the direction of the development of signal processing algorithms, which resulted in an extremely elaborate and powerful signal processing paradigm centered around the xe2x80x9cminimalistxe2x80x9d representation of signals by the Nyquist rate samples. This paradigm is usually referred to as xe2x80x9csignal processing based on harmonic analysis.xe2x80x9d
However, such xe2x80x9cminimalistxe2x80x9d approach to signal representation, free of any redundancy, need not always be optimal. Specifically, the standard signal processing operators act on sequences of values of the input signal at consecutive (Nyquist rate spaced) sampling points which are within the support of an appropriate window. These values are stored in some form of a shift register and the output value is then obtained either from these samples alone (FIR procedures) or from these samples together with the previously computed value of the signal (IIR procedures). Both types of procedures necessarily produce significant delays and/or phase-shifts in the output signal.
Moreover, although the present-day hardware is capable of accessing the information contained between the Nyquist rate sampling points, no approach based on harmonic analysis has been able to encode this information without producing troublesome proliferation of numerical data which must be stored. The concept of xe2x80x9cSignal Processor with Local Signal Behaviorxe2x80x9d had introduced a method for using the information contained between the Nyquist rate sampling points without producing troublesome proliferation of numerical data which must be stored, and without significantly increasing the computational complexity of the algorithms for subsequent processing of the data.
A need exists for signal representation and processing that does not necessarily produce delays and/or phase-shifts in the output signal. Also, a need exists for signal representation and processing that is not limited by the standard approaches. In particular, a need exists for making use of the information contained between Nyquist rate points without producing troublesome proliferation of numerical data which must be stored. Moreover, given the present-day hardware, a need exists to access this information without increasing the computational complexity of the algorithms. The present invention provides methods for the above tasks significantly improving on those described in the invention xe2x80x9cSignal Processor With Local Signal Behaviorxe2x80x9d.
The invention provides signal representation and processing that does not necessarily produce delays and/or phase-shifts in the output signal, much superior to the one described in the invention xe2x80x9cSignal Processor with Local Signal Behaviorxe2x80x9d. Also, the invention provides superior signal representation and processing that go beyond the standard approaches of harmonic analysis. In particular, the invention makes use of the information contained between Nyquist rate points and represents it in an extremely efficient way. Moreover, given the present-day hardware, the invention provides means for signal processing with low computational complexity of the algorithms.
Specifically, the invention is drawn to a method and a system for facilitated acquisition of local signal behavior parameters (LSBPs) of a band-limited (BL) signal, wherein the LSBPs encode the signal""s local behavior in between Nyquist rate points. Present-day hardware is capable of accessing the information contained between the Nyquist rate sampling points. This information can be encoded by LSBPs in a way which neither produces troublesome proliferation of numerical data which must be stored, nor does it increase the computational complexity of the algorithms for subsequent data processing.
More specifically, the values of the signal between the Nyquist rate points can be accessed using an array (or a matrix) of suitable analog, digital, or mixed signal pre-processing stages. This access can be done in a discrete format (i.e., as discrete voltages as in CCD type devices, numerical digital values provided by an oversampling A/D converter). This access can also be done in a continuous format (by various analog multipliers-integrators or an analog or mixed signal multiplier-integrator circuit as described in this invention). The values of these LSBPs can be obtained from the pre-processing devices at Nyquist rate or even sub-Nyquist rate. These LSBPs are obtained in parallel by some suitable hardware. The LSBPs describe the local signal behavior around a Nyquist rate sampling point. Additionally, the LSBPs encode local signal behavior of the signal between Nyquist rate points.
Preferably, a section of a BL signal within a sampling window is represented as a truncated series of order n at a sampling moment within the sampling window. The truncated series having n+1 LSBPs as its coefficients, encoding the signal""s local behavior between Nyquist rate points. Compared to the conventional approach that encodes a signal""s behavior by signal samples taken at Nyquist rate points, the invention encodes more accurately and more completely the behavior of the input signal. The LSBPs are solved numerically such that the interpolated values of the truncated series provide the best fit with the input signal. The LSBPs are respectively the values of chromatic differential operators of order 0 to order n evaluated at the sampling moment. As understood herein, the present embodiment is not restricted to the least-square fitting technique. In an alternative embodiment, curve fitting techniques other than least-square fit technique can also be implemented. Also as understood herein, LSBPs need not be solved by using discrete signal samples. For example, in another embodiment, LSBPs are solved by using a continuous signal section.
Alternatively, when a sampling window is constituted by two local sampling windows sharing an overlap, a section of a BL analog signal has a first subsection in the first local window and a second subsection in the second local window. In this scenario, the first subsection is first represented as a first truncated series at a first sampling moment in the first local window. This first truncated series is parametrized by n+1 coefficients that are n+1 LSBPs adapted for characterizing local signal behavior of the first subsection between Nyquist points. The second subsection is represented as a second truncated series at a second sampling moment in the second local window. This second truncated series is parametrized by m+1 coefficients that are m+1 LSBPs adapted for characterizing local signal behavior of the second subsection between Nyquist points. Numerical values of the n+1 and m+1 LSBPs are used together to produce k numerical values of the LSBPs for some k greater than n and k greater than m. These k LSBPs provide a single curve fitting over both local sampling windows. As understood herein, the present embodiment is not restricted to the least-square fitting technique. In an alternative embodiment, curve fitting techniques other than least-square fit technique are implemented. Also as understood herein, LSBPs need not be solved by using discrete signal samples. For example, in another embodiment, LSBPs are solved by using a continuous signal section.
In another embodiment, the invention is drawn to an oversampling analog/digital (A/D) converter followed by an array of multiplier-accumulator circuits which comprises in this case a data acquisition unit. The data acquisition unit is adapted for obtaining LSBPs to characterize an input signal. In particular, the data acquisition performs the steps that include representing the input signal as a truncated series (at a time t) having the LSBPs as coefficients, obtaining discrete signal samples or a continuous signal section from the input signal, and solving for the LSBPs by an approximation technique such as, for example, least-square fitting. Typically, the truncated series is formed by fundamental basis functions. Moreover, the LSBPs are values of chromatic linear operators of various orders evaluated at the time t.
In another embodiment, the invention is drawn to a analog or mixed signal multiplier-integrator circuit that includes a data acquisition unit for obtaining LSBPs to characterize an input signal. In particular, the data acquisition performs the steps that include representing the input signal as a truncated series (at a time t) having the LSBPs as coefficients, obtaining discrete signal samples or a continuous signal section from the input signal, and solving for the LSBPs by an approximation technique such as, for example, least-square fitting. Typically, the truncated series is formed by fundamental basis functions. Moreover, the LSBPs are values of chromatic linear operators of various orders evaluated at the time t. In particular, this circuit can be obtained by combining a multiplying digital to analog converter followed by an analog integrator. More specifically, the input signal is used as a variable reference voltage of the multiplying D/A converter, whose digital input is supplied by a properly clocked digital values of a fixed function. These digital values can be stored in a memory for which they are sent to the above mentioned D/A converter timed with a clock whose speed corresponds to an over-sampling frequency with respect to the input signal. The output of this D/A converter is then fed to the analog integrator circuit whose output is sampled at the end of each integration period. The length of this integration period depends on the number of LSBPs being acquired. After sampling, the integrator is reset, and the cycle is repeated.
In yet another embodiment, the invention is drawn to a signal processing system for processing LSBPs obtained by the steps that include representing the input signal as a truncated series having the LSBPs as coefficients, obtaining discrete signal samples or a continuous signal section from the input signal, and solving for the LSBPs by an approximation technique such as, for example, least-square fitting. Typically, the truncated series is formed by fundamental basis functions. Moreover, the LSBPs are values of chromatic linear operators of various orders evaluated at the time t.
The present invention significantly improves the mentioned one, by: increasing accuracy, reducing the requirements for data storage, and by allowing simpler algorithms for signal processing.